Charles K. Fisher

Constructing Ensembles for Intrinsically Disordered Proteins

The relatively flat energy landscapes associated with intrinsically disordered proteins makes modeling these systems especially problematic. A comprehensive model for these proteins requires one to build an ensemble consisting of a finite collection of structures, and their corresponding relative stabilities, which adequately capture the range of accessible states of the protein. In this regard, methods that use computational techniques to interpret experimental data in terms of such ensembles are an essential part of the modeling process. In this review, we critically assess the advantages and limitations of current techniques and discuss new methods for the validation of these ensembles.

Identifying Keystone Species in the Human Gut Microbiome from Metagenomic Timeseries Using Sparse Linear Regression

Human associated microbial communities exert tremendous influence over human health and disease. With modern metagenomic sequencing methods it is now possible to follow the relative abundance of microbes in a community over time. These microbial communities exhibit rich ecological dynamics and an important goal of microbial ecology is to infer the ecological interactions between species directly from sequence data. Any algorithm for inferring ecological interactions must overcome three major obstacles: 1) a correlation between the abundances of two species does not imply that those species are interacting, 2) the sum constraint on the relative abundances obtained from metagenomic studies makes it difficult to infer the parameters in timeseries models, and 3) errors due to experimental uncertainty, or mis-assignment of sequencing reads into operational taxonomic units, bias inferences of species interactions due to a statistical problem called “errors-in-variables”. Here we introduce an approach, Learning Interactions from MIcrobial Time Series (LIMITS), that overcomes these obstacles. LIMITS uses sparse linear regression with boostrap aggregation to infer a discrete-time Lotka-Volterra model for microbial dynamics. We tested LIMITS on synthetic data and showed that it could reliably infer the topology of the inter-species ecological interactions. We then used LIMITS to characterize the species interactions in the gut microbiomes of two individuals and found that the interaction networks varied significantly between individuals. Furthermore, we found that the interaction networks of the two individuals are dominated by distinct “keystone species”, Bacteroides fragilis and Bacteroided stercosis, that have a disproportionate influence on the structure of the gut microbiome even though they are only found in moderate abundance. Based on our results, we hypothesize that the abundances of certain keystone species may be responsible for individuality in the human gut microbiome.

Explaining the Structural Plasticity of α-Synuclein

Given that α-synuclein has been implicated in the pathogenesis of several neurodegenerative disorders, deciphering the structure of this protein is of particular importance. While monomeric α-synuclein is disordered in solution, it can form aggregates rich in cross-β structure, relatively long helical segments when bound to micelles or lipid vesicles, and a relatively ordered helical tetramer within the native cell environment. To understand the physical basis underlying this structural plasticity, we generated an ensemble for monomeric α-synuclein using a Bayesian formalism that combines data from NMR chemical shifts, RDCs, and SAXS with molecular simulations. An analysis of the resulting ensemble suggests that a non-negligible fraction of the ensemble (0.08, 95% confidence interval 0.03–0.12) places the minimal toxic aggregation-prone segment in α-synuclein, NAC(8–18), in a solvent exposed and extended conformation that can form cross-β structure. Our data also suggest that a sizable fraction of structures in the ensemble (0.14, 95% confidence interval 0.04–0.23) contains long-range contacts between the N- and C-termini. Moreover, a significant fraction of structures that contain these long-range contacts also place the NAC(8–18) segment in a solvent exposed orientation, a finding in contrast to the theory that such long-range contacts help to prevent aggregation. Lastly, our data suggest that α-synuclein samples structures with amphipathic helices that can self-associate via hydrophobic contacts to form tetrameric structures. Overall, these observations represent a comprehensive view of the unfolded ensemble of monomeric α-synuclein and explain how different conformations can arise from the monomeric protein.

The Dynamic Structure of α‑Synuclein Multimers

α-Synuclein, a protein that forms ordered aggregates in the brains of patients with Parkinsons disease, is intrinsically disordered in the monomeric state. Several studies, however, suggest that it can form soluble multimers in vivo that have significant secondary structure content. A number of studies demonstrate that α-synuclein can form β-strand-rich oligomers that are neurotoxic, and recent observations argue for the existence of soluble helical tetrameric species in cellulo that do not form toxic aggregates. To gain further insight into the different types of multimeric states that this protein can adopt, we generated an ensemble for an α-synuclein construct that contains a 10-residue N-terminal extension, which forms multimers when isolated from Escherichia coli. Data from NMR chemical shifts and residual dipolar couplings were used to guide the construction of the ensemble. Our data suggest that the dominant state of this ensemble is a disordered monomer, complemented by a small fraction of helical trimers and tetramers. Interestingly, the ensemble also contains trimeric and tetrameric oligomers that are rich in β-strand content. These data help to reconcile seemingly contradictory observations that indicate the presence of a helical tetramer in cellulo on the one hand, and a disordered monomer on the other. Furthermore, our findings are consistent with the notion that the helical tetrameric state provides a mechanism for storing α-synuclein when the protein concentration is high, thereby preventing non-membrane-bound monomers from aggregating.

The transition between the niche and neutral regimes in ecology.

Significance In recent years, there has been a vigorous debate among ecologists over the merits of two contrasting models of biodiversity: the niche and neutral theories of ecology. Using two different theoretical models of ecological dynamics, we show that there is a transition between a selection-dominated regime (the niche phase) and a drift-dominated regime (the neutral phase). This is analogous to the phase diagram of water, which can be in the solid, liquid, or gas phase, depending on the temperature and pressure. Our results demonstrate how the niche and neutral theories both emerge from the same underlying ecological principles. An ongoing debate in ecology concerns the impacts of ecological drift and selection on community assembly. Here, we show that there is a transition in diverse ecological communities between a selection-dominated regime (the niche phase) and a drift-dominated regime (the neutral phase). Simulations and analytic arguments show that the niche phase is favored in communities with large population sizes and relatively constant environments, whereas the neutral phase is favored in communities with small population sizes and fluctuating environments. Our results demonstrate how apparently neutral populations may arise even in communities inhabited by species with varying traits.

Protein Structure along the Order-Disorder Continuum

Thermal fluctuations cause proteins to adopt an ensemble of conformations wherein the relative stability of the different ensemble members is determined by the topography of the underlying energy landscape. “Folded” proteins have relatively homogeneous ensembles, while “unfolded” proteins have heterogeneous ensembles. Hence, the labels “folded” and “unfolded” represent attempts to provide a qualitative characterization of the extent of structural heterogeneity within the underlying ensemble. In this work, we introduce an information-theoretic order parameter to quantify this conformational heterogeneity. We demonstrate that this order parameter can be estimated in a straightforward manner from an ensemble and is applicable to both unfolded and folded proteins. In addition, a simple formula for approximating the order parameter directly from crystallographic B factors is presented. By applying these metrics to a large sample of proteins, we show that proteins span the full range of the order–disorder axis.

Thermodynamics of statistical inference by cells.

The deep connection between thermodynamics, computation, and information is now well established both theoretically and experimentally. Here, we extend these ideas to show that thermodynamics also places fundamental constraints on statistical estimation and learning. To do so, we investigate the constraints placed by (nonequilibrium) thermodynamics on the ability of biochemical signaling networks to estimate the concentration of an external signal. We show that accuracy is limited by energy consumption, suggesting that there are fundamental thermodynamic constraints on statistical inference.

Variable habitat conditions drive species covariation in the human microbiota

Two species with similar resource requirements respond in a characteristic way to variations in their habitat—their abundances rise and fall in concert. We use this idea to learn how bacterial populations in the microbiota respond to habitat conditions that vary from person-to-person across the human population. Our mathematical framework shows that habitat fluctuations are sufficient for explaining intra-bodysite correlations in relative species abundances from the Human Microbiome Project. We explicitly show that the relative abundances of closely related species are positively correlated and can be predicted from taxonomic relationships. We identify a small set of functional pathways related to metabolism and maintenance of the cell wall that form the basis of a common resource sharing niche space of the human microbiota.

Efficient construction of disordered protein ensembles in a Bayesian framework with optimal selection of conformations.

Constructing an accurate model for the thermally accessible states of an Intrinsically Disordered Protein (IDP) is a fundamental problem in structural biology. This problem requires one to consider a large number of conformations in order to ensure that the model adequately represents the range of structures that the protein can adopt. Typically, one samples a wide range of structures in an attempt to obtain an ensemble that agrees with some pre-specified set of experimental data. However, models that contain more structures than the available experimental restraints are problematic as the large number of degrees of freedom in the ensemble leads to considerable uncertainty in the final model. We introduce a computationally efficient algorithm called Variational Bayesian Weighting with Structure Selection (VBWSS) for constructing a model for the ensemble of an IDP that contains a minimal number of conformations and, simultaneously, provides estimates for the uncertainty in properties calculated from the model. The algorithm is validated using reference ensembles and applied to construct an ensemble for the 140-residue IDP, monomeric α- synuclein.

Bayesian feature selection for high-dimensional linear regression via the Ising approximation with applications to genomics

MOTIVATION Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. RESULTS Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. AVAILABILITY AND IMPLEMENTATION An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode.